Finite Group Databasebeta

← Group #13155797

Character table — Group #13155797

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424242436363636363636363672727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212128888242424242424242424242424242424242424242424242424242424242424242422412121212121212122222466121266662
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111-1-111-1-1-1-1-1-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000220000000000000-222-2-200000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-200000000000002-2-22200000
χ11222222-122222-12-12-1222222-1-122-1-1-12-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100222-1-1-1-1-1-100220000000-1-10
χ12222222-122222-12-12-1222222-1-122-1-1-12-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2-211111100-2-20000000110
χ13222222-122222-12-12-1222222-1-122-1-1-12-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100222-1-1-1-1-1-100-2-20000000110
χ14222222-122222-12-12-1222222-1-122-1-1-12-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-2-2-211111100220000000-1-10
χ1522222-122222-12-12-1222222-12-1-1-122-1-12-1-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000002-1-122-1-1-1-1220000000-1-1000
χ1622222-122222-12-12-1222222-12-1-1-122-1-12-1-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-211-2-21111-2-2000000011000
χ1722222-122222-12-12-1222222-12-1-1-122-1-12-1-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000002-1-122-1-1-1-1-2-2000000011000
χ1822222-122222-12-12-1222222-12-1-1-122-1-12-1-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-211-2-21111220000000-1-1000
χ192222-12222-1-1222222-1-1-1-1-1-1-12-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200000000000002-1-1-1-100000
χ202222-12222-1-1222222-1-1-1-1-1-1-12-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-20000000000000-2111100000
χ212222-12222-1-1222222-1-1-1-1-1-1-12-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-20000000000000-2111100000
χ222222-12222-1-1222222-1-1-1-1-1-1-12-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112200000000000002-1-1-1-100000
χ232222-122-2-2-1-1222222-11111-1-12-1-1-1-12-1-122-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−3220000000000000-2-1-11100000
χ242222-122-2-2-1-1222222-11111-1-12-1-1-1-12-1-122-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-20000000000000211-1-100000
χ252222-122-2-2-1-1222222-11111-1-12-1-1-1-12-1-122-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-20000000000000211-1-100000
χ262222-122-2-2-1-1222222-11111-1-12-1-1-1-12-1-122-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−33333220000000000000-2-1-11100000
χ272-22-2222002-2-2-2-2-222-200002222-22-2-2-2-2-2200000000000022-2-20000002−22−22−22−22−22−222−2−222−2−222−2−222−2−222−2−222−2−22-2000000000000002-20000000
χ282-22-2222002-2-2-2-2-222-200002222-22-2-2-2-2-2200000000000022-2-20000002−2−222−22−2−22−2222−2−222−2−222−2−2−2−222−2−222−2−222-2200000000000000-220000000
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χ302-22-2222002-2-2-2-2-222-200002222-22-2-2-2-2-2200000000000022-2-2000000−22−22−22−22−22−22−2−222−2−222−2−222−2−222−2−222−2−2222-2000000000000002-20000000
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χ332-22-2-12200-11-2-2-2-222133−3−3-1-12-11-11-211-22003−33−3003−33−3-1-1110033−3−3−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-22000000000000001-1−3300000
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χ352-22-2-12200-11-2-2-2-2221−3−333-1-12-11-11-211-2200−33−3300−33−33-1-11100−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72-200000000000000-11−3300000
χ362-22-2-12200-11-2-2-2-2221−3−333-1-12-11-11-211-2200−33−3300−33−33-1-11100−3−3332−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-22000000000000001-13−300000
χ372-22-2-12200-11-2-2-2-2221−3−333-1-12-11-11-211-2200−33−3300−33−33-1-11100−3−333−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-22000000000000001-13−300000
χ382-22-2-12200-11-2-2-2-2221−3−333-1-12-11-11-211-2200−33−3300−33−33-1-11100−3−333−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72-200000000000000-11−3300000
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χ422-2-22222-22-2-2-2-222-2-22-22-22222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-22-220000000000000000000000000000000000000000000000000-220000000-220
χ432-2-2222-1-22-2-2-212-1-212-22-222-1-1-2-21112-1-11-2-1-2-2-1-1212211-111-11-11-11-10000000000000000000000003−33−33−33−33−33−3000003−333−3−3002-20000000-110
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χ5544444-2-2-4-444-2-2-2-2-2-24-4-4-4-4-2-21-2-2-2-21-2-2112222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000003-3-3300000000000000
χ5644444-2-2-4-444-2-2-2-2-2-24-4-4-4-4-2-21-2-2-2-21-2-2112222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000-333-300000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1).